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Research Papers

Distributed Operational Space Formulation of Serial Manipulators

[+] Author and Article Information
Kishor D. Bhalerao

Software Engineer
Immersive Technologies,
Perth, WA 6017, Australia;
Honorary Research Fellow,
University of Melbourne,
Melbourne, VIC 3010, Australia
e-mail: kishorb@unimelb.edu.au

James Critchley

Multibody.org,
Lake Orion, MI 48362
e-mail: James@multibody.org

Denny Oetomo

Senior Lecturer
Department of Mechanical Engineering,
University of Melbourne,
Melbourne, VIC 3010, Australia
e-mail: doetomo@unimelb.edu.au

Roy Featherstone

Consultant
Department of Advanced Robotics,
Istituto Italiano di Tecnologia,
Genova 16163, Italy
e-mail: roy.featherstone@ieee.org

Oussama Khatib

Professor
Department of Computer Science,
Stanford University,
Stanford, CA 94305
e-mail: ok@cs.stanford.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 2, 2013; final manuscript received September 9, 2013; published online October 30, 2013. Assoc. Editor: Parviz Nikravesh.

J. Comput. Nonlinear Dynam 9(2), 021012 (Oct 30, 2013) (10 pages) Paper No: CND-13-1118; doi: 10.1115/1.4025577 History: Received June 02, 2013; Revised September 09, 2013

This paper presents a new parallel algorithm for the operational space dynamics of unconstrained serial manipulators, which outperforms contemporary sequential and parallel algorithms in the presence of two or more processors. The method employs a hybrid divide and conquer algorithm (DCA) multibody methodology which brings together the best features of the DCA and fast sequential techniques. The method achieves a logarithmic time complexity (O(log(n)) in the number of degrees of freedom (n) for computing the operational space inertia (Λe) of a serial manipulator in presence of O(n) processors. The paper also addresses the efficient sequential and parallel computation of the dynamically consistent generalized inverse (J¯e) of the task Jacobian, the associated null space projection matrix (Ne), and the joint actuator forces (τnull) which only affect the manipulator posture. The sequential algorithms for computing J¯e, Ne, and τnull are of O(n), O(n2), and O(n) computational complexity, respectively, while the corresponding parallel algorithms are of O(log(n)), O(n), and O(log(n)) time complexity in the presence of O(n) processors.

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Topics: Algorithms
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References

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Chang, K., and Khatib, O., 2000, “Operational Space Dynamics: Efficient Algorithms for Modeling and Control of Branching Mechanisms,” Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 1, pp. 850–856.
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Featherstone, R., 2010, “Exploiting Sparsity in Operational-Space Dynamics,” Int. J. Robotics Res., 29(10), pp. 1353–1368. [CrossRef]
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Jain, A., 2010, Robot and Multibody Dynamics: Analysis and Algorithms, Springer Verlag, Berlin.
Fijany, A., and Featherstone, R., 2013, “A New Factorization of the Mass Matrix for Optimal Serial and Parallel Calculation of Multibody Dynamics,” Multibody System Dynamics, 29(2), pp. 169–187. [CrossRef]
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Featherstone, R., 1999, “A Divide-and-Conquer Articulated Body Algorithm for Parallel O(log(n)) Calculation of Rigid Body Dynamics. Part 2: Trees, Loops, and Accuracy,” Int. J. Robotics Res., 18(9), pp. 876–892. [CrossRef]
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Figures

Grahic Jump Location
Fig. 2

Notation for a serial manipulator

Grahic Jump Location
Fig. 3

Divide and conquer algorithm

Grahic Jump Location
Fig. 4

Time comparison for computing Je and Jex

Grahic Jump Location
Fig. 5

Time comparison for computing Λe-1 and βe

Grahic Jump Location
Fig. 6

Time comparison for computing Λe-1 and βe

Grahic Jump Location
Fig. 7

Load balancing for computing Λe-1 and βe for the 512 body chain

Grahic Jump Location
Fig. 8

Time comparison for computing Λe-1 and βe

Grahic Jump Location
Fig. 9

Time comparison for computing J¯e

Grahic Jump Location
Fig. 10

Time comparison for computing Ne

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